Wow I guess "informal overview" is very different from "layperson overview", that used lots of concepts from quantum information theory. Anyway, my layperson e

Wow I guess "informal overview" is very different from "layperson overview", that used lots of concepts from quantum information theory. Anyway, my layperson explanation is as follows. Let Alice and Bob share an entangled system, but are unable to communicate normally (e.g. are lightyears apart). A ice can measure her part of the system to instantaneously affect what Bob has. However, Bob doesn't know what result Alice obtained. So, in trying to figure out what Alice did to affect his system, he has to average out Alice's possible effects on his system i.e. the possible measurements that Alice could have obtained. This averaging procedure makes it so that Bob doesn't gain any information on what system he now has. In fact, he has exactly the same information about what possible measurements he would make after Alice measured her system than information he had before Alice measured her system. Of course, if Alice was able to tell Bob the result of her measurement, then Bob wouldn't have to do any averaging and would gain information about his system. But that happening means that Alice is communicating her result to Bob classically, at slower-than-light speeds.